A $500 investment has the following payoff frequency: half of the time it will pay $350 and the other half of the time it will pay $900. Its standard deviation and value at risk respectively are:
A) $275; $150
B) $625; $275
C) $275; $350
D) $125; $500

Question

Quizplus · Accepted Answer

The standard deviation (SD) is calculated based on the variability of the payoffs around the mean. The mean payoff is (350 + 900) / 2 = $625. The differences from the mean are -275 ($350 - $625) and 275 ($900 - $625), respectively. The variance is [(275^2 + 275^2) / 2] = 75,625, and the square root of the variance gives the standard deviation, which is $275. Value at Risk (VaR) can be interpreted as the maximum expected loss over a specified period, which in this simplistic scenario can be seen as the difference between the initial investment and the lower payoff, i.e., $500 - $350 = $150.

A $500 Investment Has the Following Payoff Frequency: Half of the Time